Algorithm for 2D Interpolation

Question

I have two shapes which are cross sections of a channel. I want to calculate the cross section of an intermediate point between the two defined points. What's the simplest (relatively simple?) algorithm to use in this situation?

P.S.: I came across several algorithms like natural neighbor and poisson, which seemed complex. I'm looking for a simple solution, which could be implemented quickly.

EDIT: I removed the word "Simplest" from the title since it might be misleading

Answer 1

This is simple:

1. On each cross section draw N points at evenly spaced intervals along the boundary of the cross-section.
2. Draw straight lines from the n-th point on cross-section 1 to the n-th point on cross-section 2.
3. Take off your new cross-section at the desired distance between the old cross-sections.

Simpler still:

1. Use one of the existing cross-sections without modification.

This second suggestion might be too simple I suppose, but I bet no-one suggests a simpler one !

EDIT following OP's comment: (too much for a re-comment)

Well, you did ask for a simple method ! I'm not sure I see the same problem with the first method as you do. If the cross sections are not too weird (probably best if they are convex polygons) and you don't do anything strange such as map the left side of one cross-section to the right side of the other (thereby forcing lots of crossing lines) then the method should produce some kind of sensible cross section. In the case you suggest of a triangle and a rectangle, suppose the triangle is sitting on its base, one vertex at the top. Map that point to, say, the top left corner of the rectangle, then proceed in the same direction (clockwise or anti-clockwise) around the boundaries of both cross-sections joining corresponding points. I don't see any crossing lines, and I see a well-defined shape at any distance between the two cross-sections.